Tag Archives : Quarter Wit Quarter Wisdom

Quarter Wit, Quarter Wisdom: Work-Rate Using Joint Variation

Quarter Wit, Quarter Wisdom: Work-Rate Using Joint Variation

This week, let’s look at some work-rate questions which use joint variation. Check out the last three posts of QWQW series if you are not comfortable with joint variation.

Question 1: A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

Quarter Wit, Quarter Wisdom: Varying Jointly

Quarter Wit, Quarter Wisdom: Varying Jointly

Now that we have discussed direct and inverse variation, joint variation will be quite intuitive. We use joint variation when a variable varies with (is proportional to) two or more variables.

Say, x varies directly with y and inversely with z. If y doubles and z becomes half, what happens to x?

Quarter Wit, Quarter Wisdom: Varying Inversely

Quarter Wit, Quarter Wisdom: Varying Inversely

As promised, we will discuss inverse variation today. The concept of inverse variation is very simple – two quantities x and y vary inversely if increasing one decreases the other proportionally.

If x takes values x1, x2, x3… and y takes values y1, y2, y3 … correspondingly, then x1*y1 = x2*y2 = x3*y3 = some constant value

Quarter Wit, Quarter Wisdom: Varying Directly

Quarter Wit, Quarter Wisdom: Varying Directly

We can keep working on ‘pattern recognition’ questions for a long time and not run out of questions of different types on which it can be used. We hope you have understood the basic concepts involved. So let’s move on to another topic now: Variation.

Basically, variation describes the relation between two or more quantities. e.g. workers and work done, children and noise, entrepreneurs and start ups. More workers means more work done; more children means more noise; more entrepreneurs means more start ups and so on… These are examples of direct variation i.e. if one quantity increases, the other increases proportionally. Then there are quantities that have inverse variation between them e.g. workers and time taken. If there are more workers, time taken to complete a work will be less.

Quarter Wit, Quarter Wisdom: Pattern Recognition or Number Properties?

Quarter Wit, Quarter Wisdom: Pattern Recognition or Number Properties?

Continuing our quest to master ‘pattern recognition’, let’s discuss a tricky little question today. It is best done using divisibility and remainders logic we discussed in some previous posts. We suggest you check out these divisibility posts if you haven’t yet.

Quarter Wit, Quarter Wisdom: Pattern Recognition - Part II

Quarter Wit, Quarter Wisdom: Pattern Recognition - Part II


Today’s post comes from Karishma, a Veritas Prep GMAT instructor. Before reading, be sure to check out Part I from last week!

Last week we saw how to use pattern recognition. Today, let’s take up another question in which this concept will help us. Mind you, there are various ways of solving a question. Most questions we solve using pattern recognition can be solved using another method. But pattern recognition is a method we can use in various cases. It is something that comes to our aid when we forget everything else. If you don’t know from where to start on a question, try to give some values to the variables. You might see a pattern. You may not ‘know’ something. Even then, you can ‘figure out’ the answer because GMAT is not a test of your knowledge; it is a test of your wits. It is a test of whether you can keep your cool when faced with the unknown and use whatever you know to solve the question.

Let’s look at a question now.

Quarter Wit, Quarter Wisdom: Pattern Recognition

Quarter Wit, Quarter Wisdom: Pattern Recognition

If you are hoping for a 700+ in GMAT, you need to develop the ability to recognize patterns. GMAT does not test advanced concepts but you can certainly get advanced questions on simple concepts. For such questions, the ability to quickly observe patterns can come in quite handy. We will discuss a complicated question today which can be easily solved by observing the pattern.

Quarter Wit Quarter Wisdom: GCF and LCM of Fractions

Quarter Wit Quarter Wisdom: GCF and LCM of Fractions

Last week we discussed some concepts of GCF. Today we will talk about GCF and LCM of fractions.

LCM of two or more fractions is given by: LCM of numerators/GCF of denominators

GCF of two or more fractions is given by: GCF of numerators/LCM of denominators

Why do we calculate LCM and GCF of fractions in this way? Let’s look at the algebraic explanation first. Then we will look at a more intuitive reason.

Quarter Wit, Quarter Wisdom: Some GCF Concepts

Quarter Wit, Quarter Wisdom: Some GCF Concepts

Sometimes students come up looking for explanations of concepts they come across in books. Actually, in Quant, you can establish innumerable inferences from the theory of any topic. The point is that you should be comfortable with the theory. You should be able to deduce your own inferences from your understanding of the topic. If you come across some so-called rules, you should be able to say why they hold. Let’s discuss a couple of such rules from number properties regarding GCF (greatest common factor). Many of you might read them for the first time. Stop and think why they must hold.

Quarter Wit, Quarter Wisdom: Have a Game Plan

Quarter Wit, Quarter Wisdom: Have a Game Plan

For the past few weeks, we have been discussing conditional statements. Let’s switch back to Quant today. I have been meaning to discuss a question for a while. We can easily solve it by plugging in the right values. The only issue is in figuring out the right values quickly. The point we are going to discuss is that there has to be a plan.

Quarter Wit, Quarter Wisdom: Necessary Conditions

Quarter Wit, Quarter Wisdom: Necessary Conditions

Last week we discussed a very tricky CR question based on conditional statements. This week, we would like to discuss another CR question based on necessary conditions. Note that you don’t need to be given ‘only if’ or ‘only when’ to mark a necessary condition. The wording of the statement could imply it. You need to keep a keen eye to figure out necessary and sufficient conditions.

Quarter Wit, Quarter Wisdom: A Question on Conditional Statements

Quarter Wit, Quarter Wisdom: A Question on Conditional Statements

We hope that you have understood conditional sentences we discussed in the last post. The concept is very important and you will come across questions using this concept often. Now, let’s discuss the GMAT question we gave you last week.

Question: A newborn kangaroo, or joey, is born after a short gestation period of only 39 days. At this stage, the joey’s hind limbs are not well developed, but its forelimbs are well developed, so that it can climb from the cloaca into its mother’s pouch for further development. The recent discovery that ancient marsupial lions were also born with only their forelimbs developed supports the hypothesis that newborn marsupial lions must also have needed to climb into their mothers’ pouches.

Quarter Wit, Quarter Wisdom: Conditional Statements

Quarter Wit, Quarter Wisdom: Conditional Statements

Last week we discussed a Critical Reasoning question in detail. Today, I want to discuss a very important concept of CR — analyzing a conditional statement. You will often encounter these even though they may not be in the exact same format as the one we will discuss below. We will discuss the basic framework and then we will look at questions where this concept will be very helpful. Mind you, without this framework, it can get a little tricky to wrap your head around these questions.

Statement 1:

If you trouble your teacher, you will be punished.

What does this imply? It implies that ‘troubling your teacher’ is a sufficient condition to get punished. If you trouble, you will get punished.

Quarter Wit, Quarter Wisdom: Evaluate the Conclusion

Quarter Wit, Quarter Wisdom: Evaluate the Conclusion

At the risk of generalizing from a relatively small sample, let me say that people who are good at Quant, tend to be good at Critical Reasoning in Verbal. I certainly cannot comment about their SC and RC prowess but they are either good at CR right from the start or improve dramatically after just a couple of our sessions. The reason for this is very simple – CR is more like Quant than like Verbal. CR is very mathematical. You need to keep in mind some basic rules and based on those, you can easily crack the most difficult of problems. There is only one catch – don’t get distracted by options put there to distract you!

Today I would like to discuss a great CR question from our book. It upsets a lot of students even though it is simple – just like a GMAT question is supposed to be. Here is the question:

Quarter Wit, Quarter Wisdom: Rates Revisited

Quarter Wit, Quarter Wisdom: Rates Revisited

People often complain about getting stuck in work-rate problems. Hence, I would like to take some 700+ level questions on rate today. I have discussed the basic concepts of work-rate (using ratios) in a previous post:

Cracking the Work Rate Problems

You  might want to go through that post before you set out to work on these problems. Ensure that you are very comfortable with the relation: Work = Rate*Time and its implications: If rate doubles, work done doubles too if the time remains constant; if one work is done, rate = 1/time etc. Thorough understanding of these implications is fundamental to ‘reasoning out’ the answer.

Quarter Wit, Quarter Wisdom: Questions on Factorials

Quarter Wit, Quarter Wisdom: Questions on Factorials

Last week we discussed factorials – how we can take something common when we have factorials in some equations. Today let’s discuss a couple of questions based on factorials. They look intimidating but they are pretty simple. Factorial is all about multiplication and hence there is a high probability that you will be able to take something common and cancel something. These techniques reduce our work significantly. Hence, seeing a factorial in a question should bring a smile to your face!

Question 1: Given that x, y and z are positive integers, is y!/x! an integer?

Statement 1: (x + y)(x – y) = z! + 1

Statement 2: x + y = 121

Quarter Wit, Quarter Wisdom: Managing Factorials in Equations

Quarter Wit, Quarter Wisdom: Managing Factorials in Equations

A concept we have not yet covered in this series is factorials (though we used some factorials in the post Power in Factorials). Let’s first discuss the basics of factorials. Once we do, we will see that most factorial expressions can be easily solved using a single method: taking common!

First of all, what is (n!)?

n! = 1*2*3*4*5*6*…*(n – 2)*(n -1)*n

Let’s take some examples:

Quarter Wit, Quarter Wisdom: Successive Division

Quarter Wit, Quarter Wisdom: Successive Division

We discussed divisibility and remainders many weeks ago. Today, we will use those concepts and discuss another type of question – successive division. But before we do, you need to go through the previous related posts on division if you haven’t read them already:

Divisibility Unraveled

Divisibility Applied on the GMAT

Divisibility Applied to Remainders

Quarter Wit, Quarter Wisdom: Working on Getting the Full Picture Again!

Quarter Wit, Quarter Wisdom: Working on Getting the Full Picture Again!

Today, we will continue our discussion on why it is important to understand the workings behind seemingly miraculous shortcuts. We will use another example from probability.

Question 1: A bag contains 4 white balls, 2 black balls & 3 red balls. One by one three balls are drawn out with replacement (i.e. a ball is drawn and then put back. Thereafter, another ball is drawn). What is the probability that the third ball is red?

Quarter Wit, Quarter Wisdom: Get the Full Picture - Part II

Quarter Wit, Quarter Wisdom: Get the Full Picture - Part II

Let’s refer back to last week’s post. We discussed why it is important to fully understand what you are doing and why you are doing it, especially while using an innovative method. We talked about it using a combinatorics example.

Let’s revisit it here:

Question 1: What is the probability that you will get a sum of 8 when you throw three dice simultaneously?

We discussed the ways of obtaining various sums. The regular way of obtaining a sum of 8 is enumerating all the possibilities. An innovative way was using 7C2 (as discussed last week).

Quarter Wit, Quarter Wisdom: Get the Full Picture

Quarter Wit, Quarter Wisdom: Get the Full Picture

Today we will discuss why ‘understanding’ rather than just ‘learning’ a concept is important. Most questions can be solved using different methods. Sometimes, a particular method seems really easy and quick and we tend to ‘learn’ it without actually knowing why we are doing what we are doing. We need to understand the strengths and the weaknesses of the method before we use it. Let me elaborate with an example.

Quarter Wit, Quarter Wisdom: Three Overlapping Sets

Quarter Wit, Quarter Wisdom: Three Overlapping Sets

Today, let’s take a look at how to use Venn diagrams to solve questions involving three overlapping sets.

First, let me show you what the three overlapping sets diagram looks like.

Notice that the total comprises of the elements that do not fall in any of the three sets and the elements that are a part of at least one of the three sets.

Quarter Wit, Quarter Wisdom: A Sets Question that Upsets Many

Quarter Wit, Quarter Wisdom: A Sets Question that Upsets Many

We hope last week’s discussion improved your understanding of sets and showed you how you can come across some tricky sets questions even though the concepts seem very simple. Today, let’s further build up on what we learned last week with the help of an example.

Example: A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum  and minimum percentage of people who could have solved both the puzzles?

Quarter Wit, Quarter Wisdom: Nuances of Sets

Quarter Wit, Quarter Wisdom: Nuances of Sets

We will start with sets today. Your Veritas Prep GMAT book explains you the basics of sets very well so I am not going to get into those. If you have gone through the concepts, you know that we can use Venn diagrams to solve the sets questions.

First, let’s look at why we should focus on terminology in sets question. Thereafter, we will put up a very nice question from our very own book which is simple but takes down many people (just like a typical GMAT question):

Say, there are a total of 100 people in a housing society. There are two clubs close to the society – A and B. You are given that of the 100 people of the housing society, 60 people are members of club A and 50 people are members of club B.

Quarter Wit, Quarter Wisdom: Working like Clockwork

Quarter Wit, Quarter Wisdom: Working like Clockwork

In the last few weeks, we have gone through the concepts of relative speed. You might be surprised to know that we can use the same concept to solve some clock problems too. The reason some clock problem can be tricky is that the hour hand and the minute hand move simultaneously so handling them separately is not easy. In such questions you can easily use relative speed i.e. speed of the minute hand relative to the hour hand. Let’s try to understand this with the help of an example.

Example: In a circular clock, the minute hand is the radius of the circle. At what time is the smaller angle between the minute hand and the hour hand of the clock not divisible by 10?

Quarter Wit, Quarter Wisdom: Taking the Official GMAT Prep Test

Quarter Wit, Quarter Wisdom: Taking the Official GMAT Prep Test

Today’s post of this series is not based on Quant section of the GMAT. Instead, we will try to answer the often asked question: When should I take the two GMAT prep tests available on mba.com?

Let’s first discuss a hypothetical situation: Say, your goal is to beat a particular opponent called Mr. Dude in a game of chess in a competition being held three months from now. Over three months, you can play four friendly matches against him on a day of your choice. The results of the friendly matches are immaterial and will not be made known to any third party. What will be your strategy?

Quarter Wit, Quarter Wisdom: Moving in Circles

Quarter Wit, Quarter Wisdom: Moving in Circles

Hopefully, you are a little comfortable with the relative speed concept now. The concept can come in handy in some circular motion questions too. Today, we will show you how you can use the fundamentals we learned in the last few weeks to solve questions involving moving in a circle. Let’s try a couple of GMAT questions to put what we learned to use:

Question 1: Two cars run in opposite directions on a circular path. Car A travels at a rate of 4π miles per hour and car B runs at a rate of 6π miles per hour. If the path has a radius of 8 miles and both the cars start from point S at the same time, how long, in hours, after the cars depart will they meet again for the first time after leaving?

Quarter Wit, Quarter Wisdom: Some Tricky Relative Speed Concepts

Quarter Wit, Quarter Wisdom: Some Tricky Relative Speed Concepts

As promised, we tackle some 700+ level questions today. Mind you, these questions are not your typical GMAT type questions. The reason we are discussing them is that they look mind boggling but are easily workable when the concepts of relative speed are used. They give insights that help you understand relative speed. Once you are good with the concepts, you can solve most of the relative speed based questions easily.

Quarter Wit, Quarter Wisdom: Questions on Speeding

Quarter Wit, Quarter Wisdom: Questions on Speeding

We discussed the concepts of relative speed in GMAT questions last week. This week, we will work on using those concepts to solve questions. The questions we take today will be 600-700 level. I intend to take the 700+ level questions next week (don’t want to scare you away just yet!). Let’s get going now.

Quarter Wit, Quarter Wisdom: Speeding, Relatively

Quarter Wit, Quarter Wisdom: Speeding, Relatively

Let’s look at the concept of relative speed today. A good understanding of relative speed can be very useful in some questions. If you don’t use relative speed in these GMAT questions, you can still solve them but they would be rather painful to work through (they might need multiple variables and you know my policy on variables – use one, if you must)

Quarter Wit, Quarter Wisdom: Some Inequalities, Mods and Sets

Quarter Wit, Quarter Wisdom: Some Inequalities, Mods and Sets

Today, let’s look at a question that involves inequalities and modulus and is best understood using the concept of sets. It is not a difficult question but it is still very tricky. You could easily get it right the first time around but if you get it wrong, it could take someone many trials before he/she is able to convince you of the right answer. Even after I write a whole post on it, I wouldn’t be surprised if I see “but I still don’t get it” in the comments below!

Quarter Wit, Quarter Wisdom: Questions on Inequalities

Quarter Wit, Quarter Wisdom: Questions on Inequalities

Now that we have covered some variations that arise in inequalities in GMAT problems, let’s look at some questions to consolidate the learning.

We will first take up a relatively easy OG question and then a relatively tougher question which looks harder than it is because of the use of mods in the options (even though, we don’t really need to deal with the mods at all).

Quarter Wit, Quarter Wisdom: Inequalities with Complications - Part I

Quarter Wit, Quarter Wisdom: Inequalities with Complications - Part I

Last week we learned how to handle inequalities with many factors i.e. inequalities of the form (x – a)(x – b)(x – c)(x – d) > 0. This week, let’s see what happens in cases where the inequality is not of this form but can be manipulated and converted to this form. We will look at how to handle various complications.

Quarter Wit, Quarter Wisdom: Inequalities with Multiple Factors

Quarter Wit, Quarter Wisdom: Inequalities with Multiple Factors

Students often wonder why ‘x(x-3) < 0’ doesn’t imply ‘x < 0 or (x – 3) < 0’. In this post, we will discuss why and we will see what it actually implies. Also, we will look at how we can handle such questions quickly.

When you see ‘< 0’ or ‘> 0’, read it as ‘negative’ or ‘positive’ respectively. It will help you think clearly.

So the question we are considering today is:

Quarter Wit, Quarter Wisdom: Some Tricky Standard Deviation Questions

Quarter Wit, Quarter Wisdom: Some Tricky Standard Deviation Questions

Last week we promised you a couple of tricky standard deviation (SD) GMAT questions. We start with a 600-700 level question and then look at a 700 – 800 level one.

Question 1: During an experiment, some water was removed from each of the 8 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 20 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

Statement 1: For each tank, 40% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

Statement 2: The average volume of water in the tanks at the end of the experiment was 80 gallons.

Quarter Wit, Quarter Wisdom: Dealing with Standard Deviation - Part II

Quarter Wit, Quarter Wisdom: Dealing with Standard Deviation - Part II

This week, we pick from where we left last week. Let’s discuss the last 3 cases first.

Question: Which set, S or T, has higher SD?

Case 5: S = {1, 3, 5} or T = {1, 3, 3, 5}

The standard deviation (SD) of T will be less than the SD of S. Why? The mean of 1, 3 and 5 is 3. If you add another 3 to the list, the mean stays the same and the sum of the squared deviations is also the same but the number of elements increases. Hence, the SD decreases.

Quarter Wit, Quarter Wisdom: Dealing with Standard Deviation

Quarter Wit, Quarter Wisdom: Dealing with Standard Deviation

We will work our way through the concepts of Standard Deviation (SD) today. Let’s take a look at how you calculate standard deviation first:



Ai – The numbers in the list

Aavg – Arithmetic mean of the list

n – Number of numbers in the list

Quarter Wit, Quarter Wisdom: A Range of Questions

Quarter Wit, Quarter Wisdom: A Range of Questions

Let’s discuss the idea of “range” today. It is simply the difference between the smallest and the greatest number in a set. Consider the following examples:

Range of {2, 6, 10, 25, 50} is 50 – 2 = 48

Range of {-20, 100, 80, 30, 600} is 600 – (-20) = 620

and so on…

Quarter Wit, Quarter Wisdom: Mean Questions on Median

Quarter Wit, Quarter Wisdom: Mean Questions on Median

As promised, we discuss medians today! Conceptually, the median is very simple. It is just the middle number. Arrange all the numbers in increasing/decreasing order and the number you get right in the middle, is the median. So it is quite straight forward when you have odd number of numbers since you have a “middle” number. What about the case when you have even number of numbers? In that case, it is just the average of the two middle numbers.

Median of [2, 5, 10] is 5

Median of [3, 78, 102, 500] is (78 + 102)/2 = 90

Quarter Wit, Quarter Wisdom: Application of Arithmetic Means

Quarter Wit, Quarter Wisdom: Application of Arithmetic Means

Last week we discussed arithmetic means of arithmetic progressions in GMAT math problems. Today, let’s see those concepts in action.

Question 1: If x is the sum of the even integers from 200 to 600 inclusive, and y is the number of even integers from 200 to 600 inclusive, what is the value of x + y?